"What you found is a football!"

Written by Liu Dun

One day in September 1985, Harold Kroto of the University of Sussex in the UK was about to end his short visit to Rice University in Texas, and before leaving, he invited several American colleagues to a farewell dinner. There was only one topic at the table: Does the atomic cluster C60 composed of 60 carbon atoms exist? If so, what is its structure? Kroto and the invitees drew different three-dimensional figures on napkins, but the results were inconclusive.

Over the past year or so, Kroto, Robert Curl, Richard Smalley and others from Rice University have been working on exploring the structure of a large carbon molecule. Their experimental team used a cluster generator invented by Smalley to detect microwave signals of C60 and some similar carbon atom clusters. These signals are highly similar to those captured by Kroto in certain areas of space through radio telescopes. The question is, how do so many carbon atoms combine to form a stable structure? People naturally think of the two most common forms of carbon - graphite and diamond. Graphite is composed of many layers of carbon atoms arranged in hexagons. Can a large net with a basic hexagonal structure be bent up (through changes in pressure, temperature or the addition of impurities) to form a sphere? At first, Kroto and others thought about it along this line of thought. However, at dinner that day, he suddenly remembered a cardboard toy in his Sussex home. It was a starry sky model he bought for his son that year. He vaguely remembered that there were pentagons on it in addition to hexagons.

Back at Cole's house, Kroto thought of the toy again and hesitated whether to call his wife and ask her to count whether there were exactly 60 vertices on the starry sky. Cole advised him not to wake his wife up because it was just dawn in England and there was no such a coincidence.

James R. Heath, another structural chemist who attended the dinner, and his wife were also not idle. On the way home, they bought a bag of gummy bears and toothpicks at a grocery store. When they got home, they couldn't wait to build a model. They used gummy bears to represent carbon atoms and toothpicks to represent connecting bonds. They first arranged a hexagon similar to the basic structure of graphite, and then tried hard to build a closed structure, but to no avail.

Smalley was the most hands-on person. After returning home, he worked on the computer for a while, but still could not come up with anything. Then he simply took out a pen, paper, scissors and glue and started doing children's crafts. He first cut out some congruent regular hexagons, and then glued them together edge to edge, trying to make a closed spherical structure. In the end, he realized that this was impossible. It was past midnight, but Smalley was getting more and more sleepless. He took out a bottle of beer from the refrigerator, and after drinking a glass of beer, he suddenly remembered the toy model that Kroto mentioned - yes, why not try a pentagon? He made a bunch of regular pentagons with the same side length and started working again. He started with a pentagon and glued a hexagon on each side of it. The paper structure easily bent upward into a bowl shape. At this time, Smalley was encouraged and vaguely felt that this combination could be repeated. Then he added 5 pentagons and 5 hexagons at intervals on the edge of the bowl-shaped structure to form a hemispherical object. Then he continued to add more pentagons and hexagons, always maintaining the pattern of five hexagons around each pentagon, and finally pieced together a perfect polyhedron structure that was close to a sphere. There were 12 regular pentagons and 20 regular hexagons in total. Yes, this should be the structure of C60!

The next morning, Smalley took his masterpiece to the university and called all the team members on the way to the office. When he threw the paper ball he had made all night on the coffee table, everyone was stunned. Kroto confirmed that the starry sky model in his home looked like this, and the cautious Cole began to test whether each carbon atom on the model met the bonding conditions. In the end, everyone unanimously agreed that this was the new carbon molecular structure they were looking for.

Left: Smalley's paper model of C60, on which Kroto and Cole put labels to indicate double bonds to test whether each carbon atom meets the bonding conditions. Right: The polyhedron star dome teaching aid stored in Kroto's home, tens of thousands of kilometers away, was later found to be exactly the same as Smalley's model.

Mathematicians would know something with such perfect symmetry. Smalley thought he should call the head of the mathematics department, Vico. After describing the construction of the model, he heard Vico's congratulations on the other end of the phone. He might be an old man, and then he did not forget to add: "Children, what you have discovered is a football!" In fact, if these chemists had consulted mathematicians earlier, they might have taken fewer detours, because according to the Euler formula of polyhedrons, convex polyhedrons composed entirely of hexagons do not exist. [Appendix: If they can find another knowledgeable mathematical historian, the other party may also tell them: A polyhedron surrounded by two (or three) congruent regular polygons is called a semi-regular polyhedron. It is said that Archimedes of ancient Greece has discovered a total of 13 different semi-regular polyhedrons (just as Plato or his school knew a total of 5 different regular polyhedrons), so it is called "Archimedean polyhedron" (Archimedean polyhedra). The structure of C60 is also an Archimedean body. ]

Once it was revealed, everyone was in tears. Yes, a modern football is made of 20 (white) hexagons and 12 (black) pentagons, and it has exactly 60 vertices. Heath excitedly ran to a nearby sports store and brought back a real football. Coincidentally, that day was his birthday. After some discussion, everyone decided to adopt Kroto's suggestion and named this new molecule "Fullerene" because the design of the geodesic dome by American architect Buckminster Fuller had provided inspiration for their discussion.

Fuller's dome for the U.S. Pavilion at the 1967 Montreal World's Fair

In 1996, Kroto, Cole and Smalley won the Nobel Prize in Chemistry for their discovery of fullerenes. Their contribution was not only the discovery of the existence of the soccer ball-shaped fullerene C60 and the determination of its structure, but also the opening of a new direction for the study of "spherical chemical structures". C60 is just one of the huge fullerene family. More and more fullerenes are being discovered or produced in the laboratory. Fullerenes and their derivatives have been widely used in superconductivity, nanomaterials, "large carbon structure" design, and virology, and have also provided strong support for the theory of cosmic evolution.

From left to right: Croto, Curle, Smalley

The cover of Nature magazine in November 1985 reported that Cole, Kroto and Smalley had discovered C60 fullerene

All these are stories told in the book "Perfect Symmetry" (written by Baggott, translated by Li Tao and Cao Zhiliang, published by Hai Science and Technology Education Press).

This article was originally published in Southern Weekend on August 30, 2018, and was authorized by the author to be published in Fanpu with slight modifications.

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